Lx(f) = -i hbar (y d(f,z) - z d(f,y)) Ly(f) = -i hbar (z d(f,x) - x d(f,z)) Lz(f) = -i hbar (x d(f,y) - y d(f,x)) f = psi(x,y,z) "Angular momentum operators" Lx(f) Ly(f) Lz(f) "Verify commutation relations (1=ok)" Lx(Ly(f)) - Ly(Lx(f)) == i hbar Lz(f) Ly(Lz(f)) - Lz(Ly(f)) == i hbar Lx(f) Lz(Lx(f)) - Lx(Lz(f)) == i hbar Ly(f) -- angular momentum operators in spherical coordinates Lx(f) = i hbar expsin(phi) d(f,theta) + i hbar expcos(theta) / expsin(theta) expcos(phi) d(f,phi) Ly(f) = -i hbar expcos(phi) d(f,theta) + i hbar expcos(theta) / expsin(theta) expsin(phi) d(f,phi) Lz(f) = -i hbar d(f,phi) "Verify commutation relations in spherical coordinates (1=ok)" f = psi(r,theta,phi) Lx(Ly(f)) - Ly(Lx(f)) == i hbar Lz(f) Ly(Lz(f)) - Lz(Ly(f)) == i hbar Lx(f) Lz(Lx(f)) - Lx(Lz(f)) == i hbar Ly(f)

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